Metamaterials are artificial composites that achieve material performance beyond the limitation of uniform materials and exhibit properties not found in naturally-formed substances. Such artificially structured materials are typically constructed by patterning or arranging a material or materials to expand the range of electromagnetic properties of the material.
When an electromagnetic wave enters a material, such as a metamaterial, the electric and magnetic fields of the wave interact with electrons and other charges of the atoms and molecules of the material. These interactions alter the motion of the wave changing the electromagnetic wave propagation properties in the material, e.g., velocity, wavelength, direction, dispersion, impedance, index of refraction, and the like. The velocity and wavelength of the electromagnetic wave in a material is controlled by two parameters: electric permittivity (ε) and magnetic permeability (μ). The velocity of an electromagnetic wave in the material is governed by:
                    c        =                  1                                    μ              ⁢                                                          ⁢              ɛ                                                          (        1        )            and the wavelength of an electromagnetic wave in the material is governed by:
                    λ        =                              c            f                    =                      1                          f              ⁢                                                μ                  ⁢                                                                          ⁢                  ɛ                                                                                        (        2        )            where f is the frequency of the electromagnetic wave. As shown by equations (1) and (2), increasing the value of μ and/or ε in a metamaterial is one way to control electromagnetic wave propagation properties in the metamaterial, such as reducing the velocity and wavelength.
The dimensions of an antenna are usually determined by the frequency at which the antenna is designed to function. An ideal antenna is some multiple (or half multiple) of the electromagnetic wavelength such that the antenna can support a standing wave. Antennas usually do not satisfy this constraint because designers either require the antenna to be smaller than a particular wavelength, or the antenna is simply not allotted the required volume in a particular design. When an antenna is not at its ideal dimensions, reflections from the edges of the antenna interfere with the standing wave and the antenna loses efficiency. An antenna, or guided wave structure, is often used to capture information encoded on an electromagnetic wave. However, if the antenna is smaller than an incoming electromagnetic wavelength, the information is captured inefficiently and considerable power is lost. One way to overcome the aforementioned problems is to use a metamaterial and reduce the wavelength of the electromagnetic wave in the metamaterial of the antenna by increasing the value of μ and/or ε for the metamaterial of the antenna. Increasing μ and/or ε in a metamaterial allows for making ultra-miniature antennas, as well as also other smaller devices, such as phase shifters, beam steering devices, and the like.
Every material has a different value for μ and ε. One approach used in conventional metamaterials to reduce the wavelength or velocity in a material is to choose materials that naturally have high values for ε and μ. But, this often results in an impedance mismatch at the edges of the material. Impedance can be thought of as the resistance of a material to the propagation of electromagnetic waves. Impedance is described by the ratio of the magnetic component of an electromagnetic wave to its electrical component. In a non-conducting electromagnetic medium, this relationship is described by:
                    Z        =                  μ          ɛ                                    (        3        )            
At the interface between two materials, it is the difference in impedances that leads to reflections and energy loss. When electromagnetic waves propagate through a material, some of the energy of electromagnetic waves turns to thermal energy. Choosing a material with a high value for ε is one way to reduce thermal losses. Ideally, one would decrease the wavelength in the metamaterial by choosing a high value for μ and choosing a high value for ε to reduce thermal losses while keeping the ratio of μ/ε the same to reduce impedance mismatch and reflections. However, in practice, this is not currently possible with conventional materials.
If the impedances of the two materials are matched, the energy exchange across the interface will be perfectly efficient. Therefore, one of the benefits of engineered materials and metamaterials is the ability to vary the permittivity and permeability of the material to achieve the desired wavelength, while keeping optimal impedance.
Any variation in a material on a length scale smaller than the wavelength of an incident electromagnetic wave looks as a continuous material to that electromagnetic wave. One way to engineer metamaterials is to include composite structures inside the material and keep the spacing between the structures small compared to the wavelength of the electromagnetic wavelength. Thus, composite metamaterials can be designed by combining materials where ε is optimized in one material and μ is optimized in another material such that the scales of the two materials are smaller than the wavelength of the electromagnetic wave. An electromagnetic wave therefore interacts with the composite as if it were a bulk material with the desired values of μ and ε.
One conventional metamaterial uses small circuits spaced smaller than the wavelength of an incoming electromagnetic wave. See “Composite Right/Left-Handed Transmission Line Metamaterials”, IEEE Microwave Magazine, 2004, ITOH, incorporated herein by reference. As disclosed therein, a metamaterial is comprised of periodic arrays of resonating elements, e.g., capacitor-inductor elements, arranged to couple effectively into an antenna or guided wave structure that modifies an electromagnetic wave.
However, the disadvantages of this metamaterial include electrical losses in the structure, the challenge of attaining the high inductance required to operate at the desired frequencies, and the large size of individual elements. These disadvantages limit the range of resonant frequencies that can be achieved and the minimum size the structure can achieve.
Another way to control electromagnetic wave propagation properties in a material is to use electromechanical resonators to convert the electrical energy of electromagnetic wave to mechanical energy, e.g., vibrations, and store the mechanical energy therein. If the electromechanical resonators were spaced in a medium such that the spacing between the electromechanical resonators was small compared to the wavelength of the electromagnetic wave, an innovative new electromagnetic composite metamaterial could be achieved.